A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground,away from the wall at the rate of 10 cm/s. How fast is the angle between the ladder and the ground decreasing when the foot of the ladder is 2 m away from the wall?

Options

A. `1/10` rad/s
B. `1/20` rad/s
C. 20 rad/s
D. 10 rad/s

Answer

B

Explanation

Let the angle between floor and the ladder be `theta`.
Let AB=x and BC= y cm
`therefore sintheta=x/500` and `costheta=y/500`
`rArr x=500sintheta "and" y=500costheta`
Also, `(dx)/(dt)=10`cm/s
`rArr (d(theta))/(dt)=10/(500costheta)=1/(50costheta)`
For y=2m = 200cm,
`(d(theta))/(dt) =1/(50.y/500)=10/y`
`=10/200=1/20` rad/s